It appears that some of the Ahaadith on which the Fuqaha base the masaa-il are dhaeef (weak) according to the later Muhadditheen.

Answer

The Aimmah-e-Mujtahideen/ Fuqaha are not subservient to the Muhadditheen. They are not bound by the rules of the later Muhadditheen. Every Hadith which constitutes a Mustadal (Basis for the formulation of a mas'alah/hukm) enjoys the highest category of authenticity regardless of the classification of the later Muhadditheen whose function was not formulation of masaa-il. The later Muhadditheen's function was to categorize Hadith narrations in terms of the standards which they had formulated. Their function was not to test the mustadallaat of the Fuqaha. The Muhadditheen in practical life followed the Fuqaha. Thus, even if a Mustadal of the Imaam of the Math-hab is 'weak' in terms of the criterion of the Muhaddith, he (the Muhaddith) continued following the Imaam of his Math-hab. He did not cancel the mas'alah which stemmed from the Mustadal of his Imaam despite the 'weak' classification of the Hadith which constitutes the Mustadal. A Hadith could have been of the highest category of authenticity when it reached the Mujtahid Imaam, but the isnaad became weak a century later when it reached the Muhaddith.